I need to solve this problem numerically: $$ n'(t)=0.12\left(1-\frac{1}{10000}\cdot n(t)\right)\cdot n(t)-x,\\ n(0)=2000. $$
I need to find the right $x$ so that $n'(t)=0$. I know that the right answer is $x=192$ but how do I proceed the task? In what program can I set up the equation so that it tries all the values of $x$ and shows that when $x=192$ then $n'(t)=0$ ???
You can solve the problem without any numerical method:
To have $n'(0)=0$ and $n(0)=0$ you need: $$0=n'(0)=0.12\left(1-\frac{1}{10000}\cdot n(0)\right)\cdot n(0)-x=0.12\left(1-\frac{1}{10000}\cdot 2000\right)\cdot 2000-x$$ i.e:$$0=192-x$$